Food is consumed by offensive units (troops). If not enough food is available for troops, the units will abandon your city.
The rate at which food is consumed by troops is indicated in the resource tab. When the mouse is scrolled over the line for food, it is displayed as Troops Upkeep. It is also displayed in the Production report in the City Hall menu.
 Per Unit
The rate that each unit consumes is listed in the Barracks menu when the mouse pointer is placed over the unit icon. Unfortunately, the time period for the given metric is not specified.